Chapters 6-8 Study Guide
A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution?
1) If the population of grade-point averages has a normal distribution. 2) The sample has more than 30 grade-point averages.
Which of the following statistics are unbiased estimators of population parameters?
1) Sample mean used to estimate a population mean. 2) Sample variance used to estimate a population variance. 3) Sample proportion used to estimate a population proportion.
A continuous random variable has a _______ distribution if its values are spread evenly over the range of possibilities.
A continuous random variable has a uniform distribution if its values are spread evenly over the range of possibilities.
If you select a simple random sample of M&M plain candies and construct a normal quantile plot of their weights, what pattern would you expect in the graphs?
Approximately a straight line.
c. Are the logarithms of normally distributed heights also normally distributed?
No
What's wrong with the following statement? "Because the digits 0, 1, 2, . . . , 9 are the normal results from lottery drawings, such randomly selected numbers have a normal distribution."
Since the probability of each digit being selected is equal, lottery digits have a uniform distribution, not a normal distribution.
Which of the following is NOT a conclusion of the Central Limit Theorem?
The distribution of the sample data will approach a normal distribution as the sample size increases.
What does the notation z alpha indicate
The expression z alpha denotes the z score with an area of alpha to its right.
Which of the following is NOT a descriptor of a normal distribution of a random variable?
The graph is centered around 0.
Why must a continuity correction be used when using the normal approximation for the binomial distribution?
The normal distribution is a continuous probability distribution being used as an approximation to the binomial distribution which is a discrete probability distribution.
Which of the following is NOT true of the confidence level of a confidence interval?
There is a 1 minus alpha chance, where alpha is the complement of the confidence level, that the true value of p will fall in the confidence interval produced from our sample.
A point estimate
is a single value used to approximate a population parameter.
The Rare Event Rule for Inferential Statistics
states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), we conclude that the assumption is probably not correct.
The Central Limit Theorem
tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.
Annual incomes are known to have a distribution that is skewed to the right instead of being normally distributed. Assume that we collect a large (n greater than 30) random sample of annual incomes. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is large? Why or why not?
No; the sample means will be normally distributed, but the sample of incomes will be skewed to the right.
What is different about the normality requirement for a confidence interval estimate of sigma and the normality requirement for a confidence interval estimate of mu?
The normality requirement for a confidence interval estimate of sigma is stricter than the normality requirement for a confidence interval estimate of mu. Departures from normality have a greater effect on confidence interval estimates of sigma than on confidence interval estimates of mu. That is, a confidence interval estimate of sigma is less robust against a departure from normality than a confidence interval estimate of mu.
Give a brief general description of the number of degrees of freedom.
The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.
Which of the following is NOT a property of the Student t distribution?
The standard deviation of the Student t distribution is s equals 1.
Finding probabilities associated with distributions that are standard normal distributions is equivalent to
finding the area of the shaded region representing that probability.
A normal quantile plot
is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding z-score that is a quantile value expected from the standard normal distribution.
The sampling distribution of a statistic
is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
The Chi-square distribution
is used to develop confidence interval estimates of variances or standard deviations.
A critical value, z alpha, denotes the
z-score with an area of alpha to its right
